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Electrostatic Force and Equilibrium Consider a rhombus with side of length L. The rhombus has two pair of...

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Physics

Electrostatic Force and Equilibrium

Consider a rhombus with side of length L. The rhombus has twopair
of equal interior angles. Label one of these pair θ and the otherφ. Four
identical, positive point charges, q are placed on the vertices ofthe rhombus.
Draw the configuration.

a) Obtain a symbolic expression for the electric field at one ofthe vertices
(your choice) and then at an adjacent vertex (Do you now know theelectric
field at all of the vertices? Why/why not?). Does it matter thatthere is a
charge at the vertex? Comment on the direction of the electricfield at your
two vertices. Does this make sense? Why?

b) We now allow the angles to vary, subject to the constraintthat the figure
must remain a rhombus. Label one of the vertices P. What θ valueand φ
value, (in degrees), minimizes the electric field at P . Hint: Youshould only
have to do one minimization, as there is a constraint between θ andφ.

c) Plot the magnitude of the electric field at P as a functionof the angle
opposite P ( This will be θ or φ depending on how you labeled yourfigure).

Please show your work and explanation. Thanks for your help.

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